You do not need to purchase a router from verizon fios, the only time you need their router, is if you also use their TV service , since for some reason, it gets everything directly from the ONT except the on-demand content and guide data, in which case, you connect the verizon router behind the actual good router that you want to use. (just change its local IP to anything other than 192.168.1.1, and then disable its DHCP, then connect it as LAN to LAN.
If you need the remote access functions on the DVR, then you will also need to forward ports 69, 1701, 35000, 63145 to the DVR.